How to work with percentages - HSPT Math

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Question

Helen wants to buy a dress for a party. It is on sale for 37% off. How much does the dress currently costs, if its original price was $45.00?

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Answer

First, multiply 45 by 0.37:

Then, subtract that amount from 45.00 to find the sale price:

Answer: The dress' sale price is $28.35.

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Question

A restaurant is having a sale and lowering their prices by 20%. If an average meal for two normally costs $62.00, what will it costs under the current sale?

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Answer

Multiply:

Then, subtract that amount from the original price:

Answer: $49.60

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Question

What is $3 \frac{1}{2}$ decreased by 40%?

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Answer

Decreasing a number by 40% is equivalent to taking 60% of a number, which in turn is equivalent to multiplying it by

$\frac{60}{100} = \frac{60 \div 20}{100 \div 20} = \frac{3}{5}$ .

$3 \frac{1}{2}$ decreased by 40% is the product of $3 \frac{1}{2}$ and $\frac{3}{5}$ :

$3 \frac{1}{2} \times \frac{3}{5}$

$= \frac{3 \times 2 + 1}{2} \times \frac{3}{5}$

$= \frac{7}{2} \times \frac{3}{5}$

$= \frac{7\times 3 }{2\times 5}$

$= \frac{21 }{10}$

$21 \div 10 = 2 \textup{ R }1$ , so the correct response is $2 \frac{1 }{10}$ .

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Question

6 decreased by what percent is $4\frac{2}{3}$ ?

Select the closest answer.

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Answer

The difference of 6 and $4\frac{2}{3}$ is

$6 - 4\frac{2}{3}$

$= \frac{6 \times 3}{3} - \frac{4 \times 3+ 2}{3}$

$= \frac{18}{3} - \frac{14}{3}$

$= \frac{18-14}{3}$

$= \frac{ 4}{3}$ .

Therefore, 6 is being decreased by $\frac{ 4}{3}$ ; to find out what percent this is of 6, we calculate:

$\frac{\frac{ 4}{3}}{6} \times 100 %$

$=\left ( \frac{ 4}{3} \div 6 \right ) \times 100 %$

$=\left ( \frac{ 4}{3} \times \frac{1}{6} \right ) \times 100 %$

$=\left ( \frac{ 2}{3} \times \frac{1}{3} \right ) \times \frac{100 }{1}%$

$=\left ( \frac{ 2}{3} \times \frac{1}{3} \right ) \times \frac{100 }{1}%$

$=\left ( \frac{ 2 \times 1 \times 100}{3 \times 3 \times 1} \right ) %$

$= \frac{ 2 00}{9} %$

$2 00 \div 9 = 22 \textup{ R 2}$ , so

$\frac{ 2 00}{9} % = 22\frac{ 2 }{9} %$ .

The answer that comes closest among the four choices is 20%.

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Question

Add the percentages:

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Answer

Add the ones digit.

The ones digit is two.

Carry over the tens digit since this number is ten or greater.

Add the tens digits with the carryover.

The hundreds and the tens digit is one.

The answer is:

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Question

A class with students went on a field trip, but one of the students was absent. What percentage of students in the class went on the field trip?

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Answer

The percentage of students who attended the field trip can be found by dividing the number present by the total number of students. Here this is divided by . You then multiply by to get the percentage.

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Question

12 increased by what percent is $15\frac{1}{2}$ ?

Select the closest answer.

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Answer

The difference of $15\frac{1}{2}$ and 12 is

$15\frac{1}{2} - 12= 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}$ .

This represents an increase of

$\frac{\frac{7}{2}}{12} \times 100 %$

$= \left ( \frac{7}{2} \div 12 \right ) \times 100 %$

$= \left ( \frac{7}{2} \times \frac{1}{12 } \right ) \times \frac{100 }{1}%$

$= \left ( \frac{7}{2} \times \frac{1}{3} \right ) \times \frac{25}{1}%$

$= \frac{175}{6}%$

$175 \div 6 = 29 \textup{ R }1$ , so this is $29 \frac{1}{6}%$ .

Tthe response closest to the correct percent is 30%.

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Question

Exactly $\frac{1}{3}$ of the plants in a garden are tomato plants. Which of the following could be the total number of plants in the garden?

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Answer

The total number of plants has to be divisible by 3. Of the answer choices, the only one that is divisible by 3 is 18. You can check this because numbers that are divisible have the sum of their digits also divisible by 3. For example,

which is divisible by 3, so 18 is divisible by 3.

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Question

A store normally sells a certain coat for $40. For the holidays it offers a sale where the new price of the coat is now $30. What percent discount is the store selling the coat for?

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Answer

The coat is $10 cheaper than normal.

$\frac{10}{40}=0.25=25%$

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Question

If Suzie's birthday cake costs $15 and it is on sale for 25% off how much will she pay at the register?

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Answer

To find the answer you must first convert the sales percentage to a decimal by moving the decimal left two places yielding

Then multiply the total cost by the decimal .

We then subtract the sales number from the original cost to get the answer:

$$15.00-$3.75=\$11.25$

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Question

Susan has a coupon for 10% off any one item at her favorite department store. There is also a storewide sale of 50% off all purchases.

If Susan wants to by a shirt originally priced at $42, how much will she pay?

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Answer

The storewide sale discounts the shirt by 50%:

$.5\times $42=$21$

Susan also has the 10% off coupon, so she's really paying 90% of the cost of the shirt:

$.9\times $21=$18.90$

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Question

The price of a suit after a 20% employee discount is $240.00. What is the original price?

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Answer

Deducting a 20% discount is the same as charging 80% of the price, so $240.00 is 80% of the original price, which we call . Just solve this equation:

$P \cdot 0.80 = 240.00$

$P = 240 \div 0.80 = 300.00$

The suit originally cost $300.00

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Question

Express $7 \tfrac{1}{2}$ % as a fraction in lowest terms.

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Answer

Put the percent over 100 and simplify as follows:

$\frac{7 \tfrac{1}{2} }{100} = 7 \tfrac{1}{2} \div 100 = \frac{15}{2} \cdot \frac{1}{100} =\frac{3}{2} \cdot \frac{1}{20} = \frac{3}{40}$

Note: all of these choices are equivalent to $7 \tfrac{1}{2}$ %; but only $\frac{3}{40}$ is in lowest terms.

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Question

There are 500 students at the high school. There are only two menu options: chicken or fish. If 15% of students ordered fish, how many students ordered chicken?

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Answer

If 15% of students ordered fish, then 85% of the students must have ordered chicken. Then multiply 85% or $.85\times 500 = 425$ .

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Question

The sales tax rate for a particular locality is 9%. How much will be paid after tax for $154.92 worth of groceries?

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Answer

Multiply the price of the groceries before tax - $154.92 - by the decimal equivalent of 9% , which is 0.09. Round this tax to the nearest hundredth (cents), then add to the price of the groceries.

Tax: $\$154.92 \cdot 0.09 \approx \$13.94$

Price after tax: $\$154.92 + $13.94 =$168.86$

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Question

A laptop computer is on sale for 40% less than the original price. If the original price is $345.00, what is the laptop's current sale price?

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Answer

First, multiply the original price by the sale percentage:

Then, subtract that amount from the original price to get the sale price:

.

The laptop's current sale price is $\$ 207.00$

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Question

To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 5,319 students, how many signatures must a student get to be on that ballot? (Nearest whole person)

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Answer

3% of 5,319 can be calculated by multiplying 5,319 by 0.03, the decimal equivalent of 3%:

$5,319 \times 0.03 = ?$

Multiply 5,319 by 3, then move the decimal point so that two digits are to the right:

$5,319 \times 3 =15,957$ ,

so

$5,319 \times 0.03 = 159.57$

Rounded to the nearest whole number, this is 160 signatures.

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Question

To get on the ballot for student body president, a student must turn in a petition with the signatures of 4% of the students. If there are 3,268 students, how many signatures must a student get to be on that ballot? (Round to the nearest whole person.)

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Answer

4% of 3,268 can be calculated by multiplying 3,268 by 0.04, the decimal equivalent of 4%:

$3,268 \times 0.04 = ?$

Multiply 3,268 by 4, then move the decimal point two places to the right:

$3,268 \times 4 =13,072$ ,

so

$3,268 \times 0.04 = 130.72$

Rounded to the nearest whole number - 131 signatures.

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Question

Refer to the above diagram. If there were 15,934 voters who were affiliated with a political party in Smith County in 2009, how many voters (nearest whole number) were there total?

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Answer

40% of the voters were registered as independents, so 60% were registered as a member of a political party. Since 60% of the voters numbered 15,934, we can find the total number of voters by setting up and solving a proportion:

$\frac{60}{100} = \frac{15,934}{N}$

$60 N = 100 \cdot 15,934$

$60 N \div 60= 1,593,400 \div 60$

which rounds to 26,557 voters.

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Question

Refer to the above graph. If there were 17,856 registered voters in Smith County in 2009, how many voters were registered as neither Republicans nor Democrats (nearest whole number)?

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Answer

2% of the voters were registered as members of other parties, and 40% were unaffiliated, so we want to calculate 42% of 17,856, or, equivalently,

$17,856 \times 0.42 = 7,499.52$

which, to the nearest whole number, rounds to 7,500 voters.

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